Tag Archives: Numbers

News that Psy’s worldwide hit “Gangnam Style” has exceeded 2.5 billion video views is astonishing. That’s two thousand five hundred million (like when my football team loses 8-0, the teleprinter helpfully adds “eight”). A Maths GCSE question could be:

Write 2,500,000,000 in standard form : Ans. 2.5 x 10 to the 9th

But where or what is Gangnam? Well, the Economist reported recently from Gangnam itself in Seoul, South Korea, where just to get into the best private tuition after-school study groups, children have to pass exams; the children are cramming for crammers. These are the Hagwon schools and the best are called Sekki (cub) – most of them in fashionable Daechi-dong in stylish Gangnam (yes that one). Students work at a level up to 5 years ahead of their age group syllabus and often arrive home tired and late after a double day in education. A law is now being proposed to ban children from studying in private tuition after 10 pm.

Children also spend their free periods at school doing extra homework for Hagwon. Parents spend 0.8 % of GDP (or a tenth of all household income) on private education, which puts South Korea top on the Private Tuition World League (Britain is 8th with 0.4% of GDP). But few parents actually admit to enrolling.

But this is what we in the West are up against – huge achievement in South East Asia. Demand for tuition is so high (sigh!) in Seoul, South Korea that no advertising is needed.

But does this have a measurable impact upon results? Well, yes. according to the latest PISA study (not the leaning tower, rather the international education benchmark for 15 year olds in 72 countries). Korea is in the top ten for Maths and reading and 11th for Science (Singapore as ever dominates). While the U.K. has climbed to 15th in Science it has dropped to 27th in Maths. A sobering thought. Should the U.K. strive to match SE Asia by copying their “learning by wrote” mastery techniques, or push on with our strategy of “real world” syllabus questions perhaps more relevant to the workplace. That’s for a future blog!

Gangnam is a fashionable district of Seoul in South Korea described as affluent and the equivalent of Beverley Hills or Chelsea. Psy wrote “Gangnam Style” as a slightly ironic social comment on Gangnam residents lifestyle.

News perhaps lost over Christmas was that national tests are to be introduced by the Goverment for times tables. up to times 12 by age 11. Momentous not so much for the fact that “3R’s back to basics” are being tested – it seems to makes sense to do so – but for the first time ever a national test is to be conducted on-line with results available immediately. It is another test for teachers to organise, so more workload, but hopefully the automation minimises administration and marking (provided the iT works !)

No doubt someone will beaver away analysing where the hotspots and coldspots are ( will x7 prove the most difficult, except in Sevenoaks? Will x2 prove the easiest, especially in Twice Brewed?). A benefit of “Big Data” analysis is that it reveals “Wisdom of the Crowds”, or “Bulk Crime” as Police would call it, where when you are able to easily consolidate data, patterns emerge, which can lead to actions being addressed.

We are all getting used to using on-line Maths coaching and testing, there are scores of websites. My own favourites are CGP Mathsbuster, BBC Bitesize, AQA AllAboutMaths, http://www.cimt.plymouth.ac.uk/ .

And last but not least http://www.mrbartonmaths.com/ where he uses “Essential Skills” diagnostic Maths quizzes with the ingenious requirement to add a few lines on “why you believe the answer is correct”, which on compilation reveals the top reasons why pupils get a particular question wrong e.g in BIDMAS. And so “Wisdom of the Crowds” helps tutors and teachers identify problem areas with the certain knowledge that a large number of other pupils also find a topic difficult.

In conclusion, how relevent is the story for GCSE? Well, the national on line test is another step on the road to automation (how far will it go?) and while Times tables will clearly not be asked directly in GCSE, many steps in GCSE questions do require a thorough knowledge of the basics, especially the non-calculator exam, otherwise slow or incorrect answers will result.

The Economist this week speculates that we are running out of combinations of letters for company names, and mentions the best and worst examples of made up names. One of the best is Google, which lead me to research its origin.

The good news is, there is a Maths angle.

The word Google comes from the googol, namely 10 to the power of 100, or 1 followed by one hundred zeros.

The founders of the company used the googol to represent the search engine idea of identifying an extremely large number of options. But the story goes that googol was
mis-spelled as google and the rest is history.

A nice GCSE question, in the new mode of “challenging”, might be:

A googol is 10 to the power 100

(a) What is a googol divided by ten to the power 98(b) Write in standard form 15 googols

These could be seen as frightening, yet easy at the same time:

(a) answer = 10² = 100
(b) answer 1.5 x ten to the power 101

The word googol itself was invented by a nine year old (why am I not surprised?) in the 1920’s. The nephew of American mathematician Edward Kasner. To get an idea of what a googol “looks like” it is similar to the ratio of the mass of an electron to the mass of the whole visible universe.

The word google in fact was mentioned before the company invention by an unlikely author, Enid Blyton. Not in “A very large number of people go the smuggler’s top” but in the term “Google Bun” in Faraway Magic Tree. Also (much more likely) Douglas Adams used the term Googleplex in the Hitchhiker’s Guide to the Galaxy, while Google itself uses “Googleplex” as the name for it’s HQ.

Googleplex is in fact the term for 10 to the power googol ( ten to the ten to the 100) which is a very large number indeed, perhaps to infinity and beyond. The mind boogles. I mean boggols. I mean boggles. in “Back to the Future 3″ the Doc says about future wife Clara ” She’s one in a billion. One in a Googleplex!”

The word googol surfaced again when it was the £1 million question in 2001 in Who Wants to Be a Millionaire?, the one where Charles Ingram was revealed to have used an accomplice.

Google (the word) is often in the news. It was the subject of an imaginary merger of the future with Amazon and subsequent war with Microsoft in (the Epic 2014 Googlezon wars).

It has officially become a verb (to Google, to search). Ironically Google the company doesn’t like this use, because it has come to mean “to search the whole web”, not just using their search engine, although most people do actually use Google as their primary search tool.

Google has been translated for instance into Chinese

After a financial reorganisation, Google the company name, has technically become “Alphabet” (a combination of word search and alpha-bet, the best algorithm choices). Personally I don’t think “Alphabet” will stick – the word will never catch on!

Finally, the Economist rated Google one of the best company names (becoming a verb clinched it). The worst? A large consultancy expensively renamed itself “Monday”, a name judged so bad that it did not last to the Friday, when it was taken over.

360 Degrees Of Billy Paul was one of the classic Philadelphia soul albums in the early 1970’s. It features the famous Gamble and Huff composition “Me and Mrs Jones”. Billy went on to record “Let Em In”, one of the few occasions, like Joe Cocker with a Little Help from My Friends, where the cover is arguably better than the original by a Beatle.

To be pedantic, Billy’s face only appears to be rotating 180°, nonetheless it is a classic album cover, and 360° features of course throughout GCSE Maths, in “bearings” questions, circular geometry, symmetry and segment analysis.

A typical foundation level question might be:

In the shape above, where is the line of symmetry? Answer is a line, drawn vertically down the middle.

Then a supplementary question about symmetry for higher level might be along the lines of:

If we then assume there is fourth hidden face at the back, and it is a 3-dimensional model, and you look down on it from the top, how many lines of symmetry are there? Answer: 4

And what is the order of rotational symmetry? Answer: 4 because there are 4 points through a rotation of 360° where the shape would look identical.

Watching The Life of Pi film again recently. Most people (OK 99.9%) of people remember the tiger, but the Mathemateer was most struck by the scene in which young Piscine Patel, tired of mockery, jumps up and announces his nickname is Pi, and what’s more can recite it to many decimal places. He writes 3.14159 …etc to many hundreds of decimal places on the board and achieves instant stardom.

Pi features in many GCSE Maths questions in formulae and it is really important for pupils to know which formulae are given in the formula sheet (for instance the volumes of spheres and cones) and which are not (quite rightly the formulae for a circle’s area and perimeter are not).

A typical higher level question might ask this:

In a full, tightly packed golf ball box there are two golf balls. What % of the volume of the box is occupied by the golf balls?

At first you think, we are not given any dimensions, how on earth can we solve this? The trick as you will increasingly see in the new syllabus is to think about a problem laterally and say, “Ok let’s call the radius r, see what happens, and start doing some calculations”. You will soon find that the volume of the box is 16 r³, while the volume of the two spheres is 8 pi r³/3 and a quick division gives you an answer of 52.4% because the “r” terms cancel out.

And finally, one more thing to remember. pi is an irrational number, which means it cannot be expressed as a whole number nor even a fraction. In fact it goes on forever, which is why Piscine is such a hero! And why it is used in “express to 4 significant figures” questions! Or why, if a GCSE question’s answer involves pi, and says “ leave as an exact answer” the pupil has to simply leave pi in the answer rather than try to work out the never ending, inexact, result. “Exam management” tips like this win points!